OCR MEI D1 2016 June — Question 5 16 marks

Exam BoardOCR MEI
ModuleD1 (Decision Mathematics 1)
Year2016
SessionJune
Marks16
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCritical Path Analysis
TypeDraw activity network from table
DifficultyModerate -0.8 This is a standard Decision Mathematics 1 critical path analysis question requiring routine application of well-practiced techniques: identifying precedences from text, drawing an activity network, calculating early/late times, and producing a resource schedule. While multi-part and requiring careful reading, it involves no novel problem-solving or mathematical insight beyond textbook methods.
Spec7.05a Critical path analysis: activity on arc networks7.05b Forward and backward pass: earliest/latest times, critical activities7.05c Total float: calculation and interpretation
5 A village amateur dramatic society is planning its annual pantomime. Three rooms in the village hall have been booked for one evening per week for 12 weeks. The following activities must take place. Their durations are shown.
ActivityDuration (weeks)
Achoose lead actors1
Bchoose rest of actors1
Cchoose dancers1
Drehearse lead actors8
Erehearse rest of actors6
Frehearse dancers6
Gprepare scenery6
Hinstall scenery1
Iprepare music2
Jmake costumes4
Kdress rehearsals2
Each activity needs a room except for activities G, I and J.
Choosing actors and dancers can be done in the same week. Rehearsals can begin after this. Rehearsing the dancers cannot begin until the music has been prepared. The scenery must be installed after rehearsals, but before dress rehearsals.
Making the costumes cannot start until after the actors and dancers have been chosen. Everything must be ready for the dress rehearsals in the final two weeks of the 12-week preparation period.
  1. Complete the table in your answer book by showing the immediate predecessors for each activity.
  2. Draw an activity on arc network for these activities.
  3. Mark on your network the early time and the late time for each event. Give the critical activities. It is discovered that there is a double booking and that one of the rooms will not be available after week 6.
  4. Using the space provided, produce a schedule showing how the pantomime can be ready in time for its first performance.
Question 5:
Part (i):
AnswerMarks Guidance
AnswerMarks Guidance
Activity table with correct immediate predecessors: A,B,C,G,I have \(-\); D has A; E has B; F has C,I; H has D,E,F,G; J has A,B,C; K has H,JB1 A, B, C, G and I
B3\(-1\) for 1 or 2 wrong rows; \(-2\) for 3 or 4 wrong rows; \(-3\) for 5 or 6 wrong rows
Part (ii)+(iii):
AnswerMarks Guidance
AnswerMarks Guidance
Activity on arcM1 activity on arc
Immediate predecessors A, B, C, I, G correctA1 immediate predecessors A, B, C, I, G
Immediate predecessors D(A), E(B), F(C,I) correctA1 immediate predecessors D(A), E(B), F(C,I)
Immediate predecessors J(A,B,C), H(D,E,F,G) correctA1 immediate predecessors J(A,B,C), H(D,E,F,G)
Immediate predecessors K(J,H) + rest correctA1 immediate predecessors K(J,H) + rest
Forward pass correctM1 forward pass
Forward pass values correct (follow through)A1\(\sqrt{}\)
Backward pass correctM1 backward pass
Backward pass values correct (follow through)A1\(\sqrt{}\)
Critical activities: A, D, H, KB1cao
Part (iv):
AnswerMarks Guidance
AnswerMarks Guidance
Schedule showing F starting at ES2, LF9B1cao F (ES2, LF9)
Remaining schedule consistent and correctB1cao rest
Example schedule:
AnswerMarks Guidance
Week1 2
CPA start time0 1
Room 1A D
Room 2B E
Room 3C
GG G
II
JJ J 
# Question 5:

## Part (i):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity table with correct immediate predecessors: A,B,C,G,I have $-$; D has A; E has B; F has C,I; H has D,E,F,G; J has A,B,C; K has H,J | B1 | A, B, C, G and I |
| | B3 | $-1$ for 1 or 2 wrong rows; $-2$ for 3 or 4 wrong rows; $-3$ for 5 or 6 wrong rows |

## Part (ii)+(iii):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Activity on arc | M1 | activity on arc |
| Immediate predecessors A, B, C, I, G correct | A1 | immediate predecessors A, B, C, I, G |
| Immediate predecessors D(A), E(B), F(C,I) correct | A1 | immediate predecessors D(A), E(B), F(C,I) |
| Immediate predecessors J(A,B,C), H(D,E,F,G) correct | A1 | immediate predecessors J(A,B,C), H(D,E,F,G) |
| Immediate predecessors K(J,H) + rest correct | A1 | immediate predecessors K(J,H) + rest |
| Forward pass correct | M1 | forward pass |
| Forward pass values correct (follow through) | A1$\sqrt{}$ | |
| Backward pass correct | M1 | backward pass |
| Backward pass values correct (follow through) | A1$\sqrt{}$ | |
| Critical activities: A, D, H, K | B1cao | |

## Part (iv):

| Answer | Marks | Guidance |
|--------|-------|----------|
| Schedule showing F starting at ES2, LF9 | B1cao | F (ES2, LF9) |
| Remaining schedule consistent and correct | B1cao | rest |

Example schedule:

| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
|------|---|---|---|---|---|---|---|---|---|----|----|----|
| CPA start time | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| Room 1 | A | D | D | D | D | D | D | D | D | H | K | K |
| Room 2 | B | E | E | E | E | E | E | F | F | | | |
| Room 3 | C | | F | F | F | F | | | | | | |
| | G | G | G | G | G | G | | | | | | |
| | I | I | | | | | | | | | | |
| | | J | J | J | J | | | | | | |

---
5 A village amateur dramatic society is planning its annual pantomime. Three rooms in the village hall have been booked for one evening per week for 12 weeks. The following activities must take place. Their durations are shown.

\begin{center}
\begin{tabular}{|l|l|l|}
\hline
\multicolumn{2}{|c|}{Activity} & Duration (weeks) \\
\hline
A & choose lead actors & 1 \\
\hline
B & choose rest of actors & 1 \\
\hline
C & choose dancers & 1 \\
\hline
D & rehearse lead actors & 8 \\
\hline
E & rehearse rest of actors & 6 \\
\hline
F & rehearse dancers & 6 \\
\hline
G & prepare scenery & 6 \\
\hline
H & install scenery & 1 \\
\hline
I & prepare music & 2 \\
\hline
J & make costumes & 4 \\
\hline
K & dress rehearsals & 2 \\
\hline
\end{tabular}
\end{center}

Each activity needs a room except for activities G, I and J.\\
Choosing actors and dancers can be done in the same week. Rehearsals can begin after this.

Rehearsing the dancers cannot begin until the music has been prepared.

The scenery must be installed after rehearsals, but before dress rehearsals.\\
Making the costumes cannot start until after the actors and dancers have been chosen.

Everything must be ready for the dress rehearsals in the final two weeks of the 12-week preparation period.\\
(i) Complete the table in your answer book by showing the immediate predecessors for each activity.\\
(ii) Draw an activity on arc network for these activities.\\
(iii) Mark on your network the early time and the late time for each event. Give the critical activities.

It is discovered that there is a double booking and that one of the rooms will not be available after week 6.\\
(iv) Using the space provided, produce a schedule showing how the pantomime can be ready in time for its first performance.

\hfill \mbox{\textit{OCR MEI D1 2016 Q5 [16]}}
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Q1 8 Q2 8 Q3 8 Q4 16 Q5 16 Q6 16